Triangle regions

A farmer wants to sell his land to raise cash. There are $N$ trees on the land, and each tree is one point in the coordinate plane. No three trees lie on a single straight line.

The farmer treats every triangular region whose corners are three different trees as a candidate for sale, so there are $\binom{N}{3}$ candidates in total.

The value of a candidate is set by $v$, the number of trees inside the triangle with the corners excluded. Since no three trees are on one line, no tree lies on a side of a triangle either. For every $v$ from $0$ to $N-3$, write a program that counts the triangular regions holding exactly $v$ trees inside.

The first line contains the number of trees $N$. ($3 \le N \le 300$)

Each of the next $N$ lines contains two integers, the $x$ coordinate and the $y$ coordinate of one tree, separated by a space. ($0 \le x, y \le 1\,000\,000$)

No three trees lie on a single straight line.

Print $N-2$ lines. On line $i$, print the number of triangular regions holding exactly $i-1$ trees inside.